Grill the ribs
Clean and oil the grill grates. For a gas grill, light the front burner to medium low and leave the back burner(s) off. For a charcoal grill, light a medium fire (300°F to 350°F) with all the coals banked to one side and the other side empty.

In a small bowl, mix 2 Tbs. salt with 2 tsp. pepper with the pimentón or cayenne, oregano, and sugar. Pat the mixture all over both sides of the ribs. Let sit at room temperature while the grill heats.

Set the ribs, meaty side up, over the cool zone of the fire and cook covered (with the vents open on a charcoal grill) until the ribs brown and become tender (a paring knife should easily slice into the meat and the ribs should sag if you hold the center up with a pair of tongs), about 1-1/2 hours.

Make the sauce
While the ribs cook, combine 2 Tbs. vinegar with the garlic and oregano in a medium bowl. Using the bottom of a small spoon, smash the garlic and oregano against the bottom and sides of the bowl until it turns into a paste with the vinegar. Whisk in the remaining vinegar, 1/3 cup water, the oil, and 2 tsp. salt.

Transfer the ribs to a carving board to rest for 5 minutes. Cut the racks (meaty side down so they’re easier to slice) into individual ribs and transfer to a plate. Whisk the sauce well, drizzle on top of the ribs, and serve.